The continuing goal of this multifaceted project is to develop and employ mathematical and physics-based methodologies which can be used to investigate complex biological structures and materials. One example from this reporting period involves the continuation of a project to provide the basis for quantitative assessment of the chemotactic response of neutrophils and other amoeboid cells. Migration of cells along gradients of effector molecules is necessary during immune response and is involved in tissue development and cancer metastasis, The experimental assessment of chemotaxis thus is of high interest, but is difficult to measure. Chemotaxis is frequently inferred by determining how many cells cross a boundary in a chemotaxis assay, for example how many cells crawl into the filter in the filter migration assay or how many cells crawl into a defined region in the under agarose assay or agarose spot assay. The major limitation of this approach is that motion is not necessarily directed by the chemoattractant gradient. To determine how reliably methods based on boundary crossing can indicate chemotactic motion of cells, we used information about the gradient sensitivity of neutrophils and MDA-MB-231 breast cancer cells to model how much gradient sensing increases the rate of boundary crossing relative to a random-motility control, and over what duration. As part of this effort, we determined the chemoattractant profile in the filter migration assay for filters of low porosity, showing that neutrophils can sense chemoattractant gradients generated in the under agarose and agarose spot assays for 12 h, whereas in the filter assay a neutrophil would be able to reliably perceive a gradient for about 10 hours. In contrast, chemotaxis of MDA-MB-231 cells, and cells with similar sensitivity to gradients, cannot be reliably measured by counting the cells in the agarose spot and under agarose assays and, whereas measurement of chemotaxis of these cells using the filter assay can be accomplished, but doing so requires stringent controls. (Manuscript in preparation.) Another of our activities involved the development of a method to track and quantify the movements of HIV viruses through dense mucus. We analyzed old images, previously obtained by time-resolved fluorescence confocal microscopy (t-FCM), and quantified the motion of fluorescently-labeled, inactivated HIV virions which had been added to samples of crude, untreated cervical mucus. After delineating the pixel locations of the fluorescent peaks associated with the viruses, we tracked the center of mass of their centroids over consecutive frames. To assess the randomness of the motion of a virus we calculated changes of its statistical mean-squared displacement (MSD). As compared to our earlier report (Boukari et al., Biomacromolecules 10:2482-8, 2009), we doubled the observation time (34 second), which provided additional insight into the overall behavior of the viruses. Half the tracked viruses appeared significantly constrained, with their MSDs being very weakly dependent on time. The others showed relative mobility with MSDs that are proportional to the sum of two terms, depicting a combination of anomalous diffusion and/or slow, flow-like behavior. The MSD data reveal plateaus attributable to possible stalling and caging of the viruses during their motion, providing quantitative information that can guide the development of physical theories to deal with the way the heterogeneity and internal stresses of the mucus affect the movement of embedded nanoparticles. (Manuscript under review.)